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1.
The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.  相似文献   

2.
 We describe the capabilities of coherent high resolution radar to observe remotely the effects of an upwelling subsurface flow on the water surface. This observation is possible because the radar radiation backscatters very strongly from surface features with dimensions similar to its wavelength, in this case X-band at 0.03 m. This technique provides imaging capability with relatively high spatial resolution (∼0.3 m) and fast time sampling (∼0.006 s) over a large surface area. The processed data reveal both the line-of-sight velocity spectrum of moving water surface features, and their water surface radar backscatter cross-section. We believe that the surface features are generated by subsurface vortices oriented normal to the surface. The vortices are advected with the bulk flow of the jet. Our radar observations of the down-stream flow from a submerged waterjet that is directed parallel to the surface are consistent with those previously measured by laser velocimetry. Received: 25 February 1994/Accepted: 16 May 1996  相似文献   

3.
Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).  相似文献   

4.
《Applied Scientific Research》1996,57(3-4):279-290
This paper presents a new technique to produce controlled stretched vortices. Intense elliptical vortices are created by stretching of an initial vorticity sheet. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the vorticity vectors. This low velocity flow enables direct observation of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile. The velocity profile is obtained with an ultrasonic pulsed Doppler velocimeter. The evolution of the central diameter of the vortices is related to the stretching. It is observed that destabilization occurs by pairing of two vortices, by hairpin deformation, and by breakdown of vortices into a “coil shape”.  相似文献   

5.
This paper is devoted to direct comparisons of related, detailed experimental and numerical studies of the non-linear, late stages of laminar-turbulenttransition in a boundary layer including flow breakdown and the beginning offlow randomization. Preceding non-linear stages of the transition process arealso well documented and compared with previous studies. The experiments wereconducted with the help of a hot-wire anemometer. The numerical study wascarried out by direct numerical simulation (DNS) of the flow employing theso-called spatial approach. Both the experiments and the DNS were performed atcontrolled disturbance conditions with an excitation of instability waves inthe flat-plate boundary layer. In the two cases, the primary disturbanceconsists of a time-harmonic, two-dimensional Tollmien--Schlichting wave thathas a very weak initial spanwise modulation. Despite somewhat differentinitial disturbance conditions used in the experiment and simulation, thesubsequent flow evolution at late non-linear stages is found to be practicallythe same. Detailed qualitative and quantitative comparisons of theinstantaneous velocity and vorticity fields are performed for twocharacteristic stages of the non-linear flow breakdown: (i) “one-spike stage” and (ii) “three-spike stage.” The twoapproaches clearly show in detail the process of development of the Γ-structure, a periodical formation of ring-like vortices, the evolution of the surrounding flow field, and the beginning of flowrandomization. In particular, it is found experimentally and numerically thatthe ring-like vortices (associated with the well-known spikes) induce somerather intensive positive velocity fluctuations (positive spikes) in thenear-wall region which have the same scales as the ring-like vortices and propagate downstream with the same high (almost free-stream) speed. The positive spikes form a new high-shear layer in the near-wall region. In the experiment the induced near-wall perturbationshave a significant irregular low-frequency component. These non-periodicalmotions play an important role in the process of flow randomization and finaltransition to turbulence that starts under the ring-like vortices in thevicinity of the peak position. Received 13 December 2000 and accepted 30 October 2001  相似文献   

6.
 A new technique to produce controlled stretched vortices is presented. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the initial vorticity. This low velocity flow enables direct observations of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile obtained with an ultra-sonic pulsed Doppler velocimeter. Several modes of destabilization are observed and include pairing of two vortices, hairpin deformation, and vortex breakdown into a coil shape. Received: 3 April 1996/ Accepted: 4 October 1996  相似文献   

7.
 This study is concerned with transition in flat plate boundary layer flow. Sets of results are obtained as follows: (1) Very clear pictures of the formation and the development of the butterfly-like structures rather than ∧-structures in the K-regime of boundary layer transition are obtained. (2) A chain of ring like vortices, which generate the high-frequency spikes on the time traces of velocity and still present periodical behaviour, at the tip of each ∧-vortex, which is the part of the butterfly-like structure, are visualized for the first time. (3) A wave-like structure is observed to occupy the whole boundary layer, extending from the near-wall region to the outer edge of the boundary layer. Received: 24 September 1998/Accepted: 24 April 1999  相似文献   

8.
Flow field analysis of a turbulent boundary layer over a riblet surface   总被引:9,自引:0,他引:9  
The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s +=25.2) and drag increasing (s +=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm2 in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s +=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y + > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s +=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000  相似文献   

9.
The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v θ)∂v θ/∂r−1 is derived, wherev θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China  相似文献   

10.
High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.  相似文献   

11.
The baseline and forced flow around a bluff body with semi-elliptical D-shape was investigated by solving the 2D Navier–Stokes equations at low Reynolds numbers. A D-shape rather than the canonic circular-cylinder was selected due to the fixed separation points in the latter, enabling to study a pure wake rather than boundary-layer control. The correlation between Strouhal and Reynolds numbers, the mean drag, the lift and drag oscillations vs. the Reynolds number and wake structure were investigated and compared to experimental and numerical data. Effects of open-loop forcing, resulting from the influence of zero-mass-flux actuators located at the fixed separation points, were studied at a Reynolds number of 150. Fluidic rather than body motion or volume forcing was selected due to applicability considerations. The motivation for the study was to quantify the changes in the flow field features, as captured by Proper Orthogonal Decomposition (POD) analysis, due to open-loop forcing, inside and outside the “lock-in” regime. This is done in order to evaluate the suitability of low-order-models based on POD modes of this changing flow field, for future feed-back flow control studies. The evolution of the natural and the excited vortices in the Kármán wake were also investigated. The formation and convection regions of the vortex evolution were documented. It was found that the forcing causes an earlier detachment of the vortices from the boundary-layers, but does not affect their circulation or convection speeds. The results of the POD analysis of the near-wake flow show that the influence of the bluff body shape (“D”-shaped versus circular cylinder) on the baseline POD wake modes is small. It was found that the eigenfunctions (mode-shapes) of the POD velocity modes are less sensitive to slot excitation than the vorticity modes. As a result of the open-loop excitation, two types of mode-shape-change were observed: a mode can be exchanged with a lower-energy mode or shifted to a low energy level. In the latter case, the most energetic mode becomes the “actuator” mode. The evolution of one-slot excitation on still fluid (“Synthetic jet”) was studied and compared to published data and to “actuator” modes with external flow present. Based on the current findings, it is hypothesized that the cross-flow velocity POD modes are suitable for feedback control of wake flow using periodic excitation, due to their low sensitivity to the excitation as compared to the streamwise velocity or vorticity modes.  相似文献   

12.
A purely alternating jet without mean mass flux and a mixed pulsed jet containing an additional blowing component were investigated by particle image velocimetry (PIV). The jets issued from a two-dimensional slit connected to a converging nozzle, opening normally from a flat wall. The pulsation was driven by a loudspeaker. The mean velocity fields were characterized by the combination of downstream directional blowing and omni-directional suction. The velocity fluctuations were dominated by contra-rotating eddy pairs synchronized with the pulsation and formed at the jet edges during blowing. Phase-synchronized measurements permit the investigation of the averaged patterns and the cycle-to-cycle fluctuations of these vortices. The mean trajectories of vortex centers during a whole injection cycle show how large lateral jet expansions are achieved. For a purely alternating jet, the expansion takes place close to the slit. For a mixed pulsed jet, the vortices develop farther from the orifice. In addition, proper orthogonal mode decomposition demonstrates that only a few modes are required to represent the main events of the flow dynamics. Received: 10 August 1999 / Accepted: 10 January 2001  相似文献   

13.
Dynamics of hairpin vortices generated by a mixing tab in a channel flow   总被引:3,自引:0,他引:3  
To better understand mixing by hairpin vortices, time-series particle image velocimetry (PIV) was applied to the wake of a trapezoidal-shaped passive mixing tab mounted at the bottom of a square turbulent channel (Re h =2,080 based on the tab height). Instantaneous velocity/vorticity fields were obtained in sequences of 10 Hz in the tab wake in the center plane (xy) and in a plane (xz) parallel to the wall. Periodically-shed hairpin vortices were clearly identified and seen to rise as they advected downstream. Experimental evidence shows that the vortex-induced ejection of the near-wall viscous fluid to the immediate upstream is important to the dynamics of hairpin vortices. It can increase the strength of the hairpin vortices in the near tab region and cause generation of secondary hairpin vortices further downstream when the hairpin heads are farther away from the wall. Measurements also reveal the existence of a type of new secondary vortice with the opposite-sign spanwise vorticity. The distribution of vortex loci in the xy plane shows that the hairpin vortices and the reverse vortices are spatially segregated in distinct layers. Turbulence statistics, including mean velocity profiles, Reynolds stresses, and turbulent kinetic energy dissipation rate distributions, were obtained from the PIV data. These statistical quantities clearly reveal imprints of the identified vortex structures and provide insight into mixing effectiveness. Received: 24 February 2000/Accepted: 24 October 2000  相似文献   

14.
The detailed flow structure behind an impulsively started circular cylinder has been investigated experimentally. The Reynolds number based on the steady state velocity and the diameter of the cylinder was 500 to 3,000. This work is unique in that unsteady spatial velocities were measured simultaneously by a quantitative visualization technique — Laser Induced Photochemical Anemometry (LIPA). The surface vorticity at g/q = π/2 and vorticity distribution behind the cylinder in the Lagrangian coordinates (i.e. coordinates fixed on the cylinder) were calculated from the measured velocities. The surface vorticity shows in the early stage of flow development a close agreement with the previous results obtained by analytical and numerical approaches. The large-field velocity and vorticity information provides an insight into the formation process of the vortices downstream of the cylinder. In addition to the quantitative information, the results of visualized flow pattern obtained by LIPA technique are also presented. A preliminary version of this paper was presented at the Twelfth Symposium on Turbulence, University of Missouri-Rolla, Sept. 24–26, 1990  相似文献   

15.
This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.  相似文献   

16.
A stereoscopic PIV (Particle Image Velocimetry) technique was used to measure the three-dimensional flow structure of the turbulent wake behind a marine propeller with five blades. The out-of-plane velocity component was determined using two CCD cameras with an angular displacement configuration. Four hundred instantaneous velocity fields were measured for each of four different blade phases, and ensemble averaged in order to find the spatial evolution of the propeller wake in the region from the trailing edge up to one propeller diameter (D) downstream. The influence of propeller loading conditions on the wake structure was also investigated by measuring the velocity fields at three advance ratios (J=0.59, 0.72 and 0.88). The phase-averaged velocity fields revealed that a viscous wake formed by the boundary layers developed along the blade surfaces. Tip vortices were generated periodically and the slipstream contracted in the near-wake region. The out-of-plane velocity component and strain rate had large values at the locations of the tip and trailing vortices. As the flow moved downstream, the turbulence intensity, the strength of the tip vortices, and the magnitude of the out-of-plane velocity component at trailing vortices all decreased due to effects such as viscous dissipation, turbulence diffusion, and blade-to-blade interaction.  相似文献   

17.
The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θv = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θv = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θv = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θv = 45°) that at the low swirl ratio (θv = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.  相似文献   

18.
Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.  相似文献   

19.
In this study, the characteristics of oscillating pressure-driven flow in a microdiffuser are examined by μPIV (micro Particle Image Velocimetry) diagnostics. Utilizing a cam-follower system, a dynamic pressure generator is built in-house to provide a time-varying sinusoidal pressure source. Three parameters are examined experimentally: the excitation frequency, the cam size, and the half-angle of the microdiffuser. Driven by oscillating pressure, we find that there exists an optimal half-angle such that maximum net flow is attained in the expansion direction. Contrarily to the prediction of hydraulics theory which only considers steady flow, flow in the microdiffuser of the optimal half-angle does not necessarily remain attached. Rather, maximum net flow can also occur in microdiffusers where vortices retain a slender shape. When vortex bubbles are slender, the μPIV results reveal that the core flow accelerates to a higher forward velocity during the first half of the cycle and flow rectification is actually enhanced. Due to the three-dimensional flow structure, fluid is drawn out of the vortices near the reattachment point to join the core flow and consequently magnifies the forward flow. As the half-angle increases, vortices become rounder and the core flow is drastically narrowed to reduce flow rectification.  相似文献   

20.
A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.  相似文献   

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